$2.$ I plan to move into a new town next year and stay there for $5$ years. I am trying to devise a plan so that I am able to provide myself with a car all the time at the minimum possible cost. The cost of a new automobile is $$20,000.$ The annual maintenance cost as a function of the age of the car is given below:

Age $01234$

Cost $10002000400060008000$

The trade$-$in values as a function of the age of the car are as follows:

Age $12345$

Value $1600014000120001100010000$

Create a shortest$-$route network to represent the problem and then use Dijkstra$$s labeling algorithm to devise my optimal strategy. What is my optimal cost? $(20$ points$).$